I'm a big fan of Barkeeper's Friend for stainless steel (it brings new life to cookware). Just make sure there isn't a finish on top of the metal that would get damaged, and test it in a non-visible location first.

I would think windex would be too harsh of a chemical and damage the material after a while. Just because it looks good and works does not means it is safe for the material. Maybe the ammonia free Windex would be ok.
–
mohlsenDec 23 '11 at 13:17

I thought the same thing. But I believe the all-surface stuff I've been using doesn't have ammonia in it, and is listed as safe for stainless. link
–
JoeFishDec 23 '11 at 14:10

I think the "don't use Windex" rule dates back to when ammonia was in it. Definitely don't use ammonia on stainless.
–
DA01Aug 27 '12 at 6:35

I use Method general purpose cleaner to get stainless steel clean. The trick is to rinse it really well because any soap left on will streak. After it's clean, I maintain my stainless steel surfaces by just wiping them down with a damp microfiber cloth. The polishes are a maintenance nightmare, avoid them all!

I used WD40 (which worked on the smudges) but I didn't like the residue of WD40. So I took the WD40 Residue off with Dawn and water - wiped with a clean towel and all the prints are gone and the WD40 residue as well.